Experimental observation of lensless coincidence fractional Fourier transform with a Gaussian Schell-model beam

A modified lensless optical system for implementing coincidence fractional Fourier transform (FRT) is proposed, and the conditions for the optical system to implement the coincidence FRT with incoherent or partially coherent light are discussed. Furthermore, we report the experimental observation of lensless coincidence FRT of an object (double slits) with a typical partially coherent beam - Gaussian Schell-model (GSM) beam. The experimental results are analyzed and agree reasonably well with the theoretical results.     

Effect of spatial coherence on the scintillation properties of a dark hollow beam in turbulent atmosphere

With the help of a tensor method, we derive an explicit expression for the on-axis scintillation index of a circular partially coherent dark hollow (DH) beam in weakly turbulent atmosphere. The derived formula can be applied to study the scintillation properties of a partially coherent Gaussian beam and a partially coherent flat-topped (FT) beam. The effect of spatial coherence on the scintillation properties of DH beam, FT beam and Gaussian beam is studied numerically and comparatively. Our results show that the advantage of a DH beam over a FT beam and a Gaussian beam for reducing turbulence-induced scintillation increases particularly at long propagation distances with the decrease of spatial coherence or the increase of the atmospheric turbulence, which will be useful for long-distance free-space optical communications.     

Propagation factor of a truncated partially coherent flat-topped beam in turbulent atmosphere

Analytical expression for the propagation factor of a truncated partially coherent flat-topped (FT) beam in turbulent atmosphere is derived based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function. Numerical results show that the radius of the aperture (i.e., truncation parameter) has strong influence on the evolution properties of the propagation factor of a truncated partially coherent FT beam, and the advantage of a truncated partially coherent FT beam over a truncated Gaussian Schell-model (GSM) beam or a truncated coherent FT beam for overcoming the turbulence-induced degradation disappears gradually with the decrease of the radius of the aperture.     

An alternative model for a partially coherent elliptical dark hollow beam

An alternative theoretical model named partially coherent hollow elliptical Gaussian beam (HEGB) is proposed to describe a partially coherent beam with an elliptical dark hollow profile. Explicit expression for the propagation factors of a partially coherent HEGB is derived. Based on the generalized Collins formula, analytical formulae for the cross-spectral density and mean-squared beam width of a partially coherent HEGB, propagating through a paraxial ABCD optical system, are derived. Propagation properties of a partially coherent HEGB in free space are studied as a numerical example.     

部分相干光对周期性局域空心光束的影响

用旋转毛玻璃和光阑把激光变成部分相干光, 再经过双轴棱锥系统把一束平行光变成两束同频率但不同径向波矢分量的无衍射贝塞尔光, 相干叠加产生了部分相干的周期性局域空心光束. 通过干涉理论与实验结果相互佐证, 得出局域空心光束的周期为2.5 mm. 进一步探究入射光场相干度对产生局域空心光束的影响, 发现随着相干度的降低局域空心光束中心暗斑与周围光强的衬比度会降低, 但不影响局域空心光束的周期以及中心暗斑尺寸.     

The propagation of radially polarized partially coherent beam through an optical system in turbulent atmosphere

The propagation of a radially polarized partially coherent beam through an optical system in turbulent atmosphere is investigated. Analytical propagation formulae for the radially polarized partially coherent beam through an optical system in turbulent atmosphere are derived, and some analyses are illustrated by numerical examples related to propagation properties of the radially polarized partially coherent beam through a double-lens system in turbulent atmosphere. It is shown that the optical system, structure constant of turbulent atmosphere and the initial coherent length have significant influence on intensity, degree of polarization and degree of coherence for radially polarized partially coherent beam.     

基于调制光束的空间相干性获得局域空心光束

 通过调制部分相干光的空间相干性,实现了局域空心光束的产生。理论上根据范西泰特-策尼克定理及标量衍射积分,构造出具有一定空间相干性的部分相干光,并研究其聚焦特性。实验上采用理论上要求的光学系统来构造具有特定空间相干性的部分相干光,并采用薄透镜聚焦部分相干光。研究表明,当构造出的部分相干光经透镜聚焦,可得到局域空心光束。研究了光学系统的参数及透镜焦距对产生局域空心光束的影响,结果显示：光阑的拦截比及透镜的焦距越大,获得的空心光束的尺寸就越大。     

A simple experimental method to generate partially coherent optical bottle beam

An experimental study is carried out to investigate a special kind of three-dimensional intensity distribution of a partially coherent optical beam known as optical bottle beam produced by using an annular aperture and lens combination (Lens Aperture System). In this paper, we are demonstrating the experimental results of our observations. The investigation also includes the effects of coherence modulation and central obstruction of the annular aperture (used in Lens Aperture System) on the resultant partially coherent optical bottle beam. The method discussed in this paper is simple and cost effective.     

非均匀关联径向偏振部分相干光的产生

从理论和实验两方面对非均匀关联径向偏振部分相干光的产生进行了研究.理论上,基于相位关联与相干度的联系,推导出了非均匀关联径向偏振部分相干光的2×2阶交叉谱密度矩阵及相干度分布.实验上,利用一个相位型液晶空间光调制器的不同区域,对入射的完全相干的径向偏振光的两个正交偏振分量分别加载随机相位调制,并实验测量了这种光束的相干度分布及其对光强分布的影响.实验结果验证了光束相干度的非均匀关联结构,并且通过改变随机相位的高斯调制半宽可以改变光束的相干性分布.研究表明,随着随机相位的高斯调制半宽的增加,光束中两点间的相干度逐渐减小,其光强分布由圆环状逐渐变化为类平顶的光强分布.这种非均匀关联的径向偏振部分相干光在激光微操纵和材料加工等领域具有一定的潜在应用价值.     

Partially coherent anomalous hollow beam and its paraxial propagation

Anomalous hollow beam is extended to the partially coherent case. Analytical propagation formulae for a partially coherent anomalous hollow beam passing through a paraxial ABCD optical system are derived. The propagation properties of a partially coherent anomalous hollow beam in free space and the focusing properties of a partially coherent anomalous hollow beam are studied numerically. It is found that the propagation and focusing properties of the partially coherent anomalous hollow beam are closely related to its initial coherence.     

Circular partially coherent flattened Gaussian beam

An alternative theoretical model called circular partially coherent flattened Gaussian beam (FGB) is developed to describe a circular partially coherent beam with a flat-topped spatial profile. Explicit expression for the propagation factor of a circular partially coherent FGB is derived. We drive the analytical formulae for the cross-spectral density and mean-squared beam width of a circular partially coherent FGB propagating through a paraxial ABCD optical system based on the generalized Collins formula. The intensity, spreading and directionality properties of a circular partially coherent FGB propagating in free space are studied as numerical examples. The propagation properties of a circular partially coherent FGB agree well with those of a partially coherent flat-topped beam reported in the literature. Thus, our model provides an alternative but reliable model for describing a circular partially coherent beam with flat-topped profile.     

基于光束的相干特性拓展双缝实验教学实验内容

对部分相干光束的双缝实验干涉条纹进行了研究。利用转动的毛玻璃以及两个透镜构成了一个简单的产生部分相干光束的光学系统,通过调整毛玻璃与两个透镜的共焦点之间的距离,可以定量地控制光束的相干性。对不同相干性的光束经过双缝干涉之后的光强进行了实验观测,发现光束的相干性会对双缝干涉条纹的衬比度产生影响,光束的相干性越低,条纹衬比度也越小。并对实验结果进行了理论模拟,理论数值模拟的结果与实验观测结果基本一致。     

Real-time recognition of microscopic phase objects

A method of image enhancement and real-time input of 3-D, microscopic phase objects into a coherent optical pattern recognition system is described. The method consists of directing a low-power laser beam into a microscope objective to produce a real, magnified, coherent image of the specimen under test. The image plane is followed by two successive Fourier transform (FT) planes. In the first FT plane, low and high frequency spatial filters, one of which is photographically produced, are used as pre-processing filters to enhance the image quality. The enhanced signal is imaged from the first FT plane to the second FT plane which contains a matched spatial filter used for specimen identification. The system does not require an expensive incoherent-to-coherent light transducer and in addition, is capable of utilizing both phase and amplitude information from 3-D objects. Examples of results are given.     

Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams through an apertured astigmatic optical system

By expanding the hard-aperture function into a finite sum of complex Gaussian functions, we derived an approximate analytical formula for a partially coherent twisted anisotropic Gaussian Schell-model (AGSM) beam propagating through an apertured paraxial general astigmatic (GA) optical system by use of a tensor method. The results obtained by using the approximate analytical formula are in good agreement with those obtained by using the numerical integral calculation. Our formulas avoid time-consuming numerical integration and provide a convenient and effective way for studying the propagation and transformation of a partially coherent twisted AGSM beam through an apertured paraxial GA optical system.     

Spectral intensity characteristics of partially coherent flattened multi-Gaussian beams with an axial shadow passing though paraxial ABCD optical systems

Based on the beam model for the flattened multi-Gaussian beams (FMGBs) with an axial shadow and partially coherent theory, the expression for cross-spectral density of partially coherent FMGBs with an axial shadow has been given, and the analytical expression for the spectral intensity of partially coherent FMGBs with an axial shadow passing through paraxial ABCD optical systems has been derived. The spectral shift of partially coherent FMGBs with an axial shadow focused by a thin lens has been analyzed quantitatively. The effects of the beam profile, spatial coherence parameter and the system parameters on the relative spectral shift have been discussed in detail. Our results show that the spectral intensity and the spectral shift of partially coherent FMGBs with an axial shadow passing through paraxial ABCD optical systems depend on the source spectral density, the generalized Fresnel number of the system, the transverse coordinate, the spatially coherence parameter, as well as the beam orders.     

Spectral shift of partially coherent flattened multi-Gaussian beams with a hole passing through ABCD optical systems

Based on flattened multi-Gaussian beam model and partially coherent theory, the expression for cross-spectral density of partially coherent flattened multi-Gaussian beam with a hole was given. The analytical expression for on-axis spectrum of partially coherent flattened multi-Gaussian beam with a hole passing through a paraxial ABCD optical system was derived. The spectral shifts of the partially coherent flattened multi-Gaussian beam with a hole propagating in free space and passing through the lens have been analyzed. The effects of the beam profile, spatial coherence parameter and the system parameters on the relative spectral shift have been discussed. Our results show that the inner radius of flattened multi-Gaussian beam with a hole determines its relative spectral shift in near field and its outer radius determines that in far field. For the flattened multi-Gaussian beam with a hole passing through a lens, the on-axis relative spectral shift changes sharply near the focal plane with the increase in Fresnel number and the spatial coherence parameter.     

Display of spatial coherence

The mutual-intensity function plays a major role in characterizing quasi-monochromatic, partially coherent optical signals. We demonstrate an optical system for displaying the mutual intensity of a one-dimensional input beam. The experimental system is based on the fact that the mutual intensity of a signal can be expressed as the ensemble averaging of a cross-correlation operation between two related optical signals. The setup consists of a Sagnac interferometer followed by an optoelectronic joint transform correlator. Experimental results demonstrate the capabilities of the mutual-intensity analyzer.     

Shaping the beam profile of a partially coherent beam by a phase aperture

By use of a tensor method, an analytical formula for a partially coherent Gaussian Schell-model (GSM) beam truncated by a circular phase aperture propagating through a paraxial ABCD optical system is derived. The propagation properties of a GSM beam truncated by a circular phase aperture in free space are studied numerically. It is found that the circular phase aperture can be used to shape the beam profile of a GSM beam and generate partially coherent dark hollow or flat-topped beam, which is useful in many applications, e.g., optical trapping, free-space optical communication, and material thermal processing. The propagation factor of a GSM beam truncated by a circular phase aperture is also analyzed.     

Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam

Orbital angular momentum of the coherent beam has been intensively studied and promises potential applications in free space optical communication. But the orbital angular momentum of partially coherent beam is not well known. In this communication the coherent-mode representation method is adopted to describe the partially coherent beam and the orbital angular momentum spectrum is introduced for the partially coherent beam. The characteristics of the orbital angular momentum spectrum of partially coherent beam are discussed. To study the influence of the partial coherence on the optical link, the channel capacity is studied, with two kinds of available mode separators included.     

Partially coherent elegant Hermite–Gaussian beam in turbulent atmosphere

Based on the extended Huygens–Fresnel integral, analytical formulas for the cross-spectral density, mean-squared beam width and angular spread of a partially coherent elegant Hermite–Gaussian (HG) beam in turbulent atmosphere are derived. The evolution properties of the average intensity, spreading and directionality of a partially coherent elegant HG beam in turbulent atmosphere are studied numerically. It is found that the partially coherent elegant HG beam with smaller initial coherence width, larger beam order and longer wavelength is less affected by the atmospheric turbulence. Compared to the partially coherent standard HG beam, the partially coherent elegant HG beam is less affected by turbulence under the same condition. Furthermore, it is found that there exist equivalent partially coherent standard and elegant HG beams, equivalent fully coherent standard and elegant HG beams, and an equivalent Gaussian–Schell-model beam may have the same directionality as a fully coherent Gaussian beam whether in free space or in turbulent atmosphere. Our results can be utilized in short and long atmospheric optical communication systems.